The shape of this 30-sided box is called a rhombic triacontahedron.
The structure of this box is made out of six identical blocks of wood with a rectangular cross-section. The diagram above illustrates the relative dimensions of each block.
The blocks get faceted with 4 compound angle cuts (31.7º at 18º) so that when the blocks are assembled, each has five faces that appear on the outside of the closed box. One of the blocks is the box top.